A(1) Field of the Invention
The invention relates to a discrete single-sideband frequency-division-multiplex arrangement as well as to a demultiplex-arrangement.
In a frequency-division-multiplex arrangement a plurality of baseband signals is processed such that they can be transmitted simultaneously in a given frequency band. Hereinafter this frequency band will be called "FDM-band". This FDM-band comprises a plurality of non-overlapping subbands. By means of some modulation process or another the frequency band of such a base band signal is shifted to a subband which is characteristic for the relevant baseband signal. The signals in the successive subbands are called channel signals. The signal in the FDM-band which is constituted by all channel signals will, as usual, be called "FDM-signal".
A known modulation process is amplitude modulation. However, amplitude modulation is not economical. For, with amplitude modulation, both sidebands of the modulated signal are transmitted.
The bandwidth required for transmitting an amplitude-modulated signal therefor is twice as large as the bandwidth which is required for the transmission of only one side-band.
As the communication density in a telecommunication system was increased, that is to say as more baseband signals had to be transmitted, it was desired to use the available FDM-band more efficiently. As a result thereof a modulation process designated as single-sideband modulation was used more and more where only one sideband, as the name implies, is transmitted. By using single-sideband modulation twice as many channel signals can be transmitted in the given FDM-band as with amplitude modulation. It is true that with single-sideband modulation an efficient manner of transmission has been realized in terms of required bandwidth, but the manner in which the single-sideband FDM-signal is generated must be made as simple and economic as is technologically possible. Particular is this true when a large number of baseband signals must be converted into a single-sideband FDM-signal.
If a frequency division multiplex arrangement is used at the transmitter side of a telecommunication system, a device must be used at its receiver end for converting the FDM-signal into the individual channel signals, and these channel signals must again be reconverted into the original baseband signals. Such a device may be called frequency-division-demultiplex arrangement. Also in this arrangement, the conversion of the FDM-signal into the original baseband signals must be as simple and economic as is technologically possible.
A(2) Description of the Prior Art
For the conversion of analog baseband signals x.sub.k (t) into an analog FDM signal y(t), a frequency-division-multiplex arrangement might, for example, comprise a plurality of modulation channels each provided with a single-sideband modulation circuit. The baseband signals x.sub.k (t) are each applied to one of the modulation channels. The single-sideband channel signals which are generated by these modulation channels are thereafter combined, which results in the desired SSB-FDM signal. A typical single-sideband modulation circuit for processing analog signals is the Weaver modulator which is described in reference 1 (see chapter D). Analog filters are used in this known single-sideband modulation circuit. The rapid development of the integrated circuit technology and the possibility of large scale integration of discrete circuits has made discrete filters much more attractive than their analog counterparts. The straight forward substitution, however, of discrete filters for analog filters results in a system which requires an undesirably high number of computational steps per second.
In the references 3, 4, 5 digital frequency-division-multiplex arrangements are described. These known arrangements are arranged for converting N digital baseband signals {x.sub.k (n)}, (k = 1, 2, . . . N; n = . . . -3, -2, -1, 0, +1, +2, . . ., which are each constituted by a series of components x.sub.k (n), and which each have associated therewith a sampling frequency 1/T, into a digital baseband single-sideband frequency-multiplex-signal {y(n)}, which is constituted by a series of components y(n), and which has associated therewith a sampling frequency 1/T.sub.1, which is greater than or is equal to the frequency N/T. The signals {x.sub.k (n)} can each be applied to the arrangement through a separate lead, but also in a TDM format. For brevity's sake, the digital frequency-division-multiplex arrangement will hereinafter be indicated by "TDM-FDM" arrangement. These arrangements can be classified into two categories:
1. The first category includes those TDM-FDM arrangements which each comprises a plurality of modulation channels to each of which a baseband signal {x.sub.k (n)} is applied. In each of these modulation channels a modulation processing is performed using a carrier signal having a carrier frequency which is characterized for the relevant modulation channel, as well as a single-sideband modulation processing operation whereby each modulation channel generates the single-sideband modulated version of its input signal {x.sub.k (n)}. The frequency spectrum of a typical single-sideband modulated version of an input signal {x.sub.k (n)} is located in a subband of the baseband FDM-signal, which subband is typical for the relevant baseband signal {x.sub.k (n)}, and is characterized by said carrier frequency. With the TDM-FDM-arrangements described in references 3, 4 and 5 the baseband signals {x.sub.k (n)} are first applied to an input circuit which comprises means for selectively modulating these signals {x.sub.k (n)} for generating discrete selectively modulated baseband signals {r.sub.k (n)} having associated therewith a sampling frequency 1/T.sub.r. In particular this selective modulation consists in that each real baseband signal {x.sub.k (n)} is converted into a complex signal {r.sub.k (n)}, wherein r.sub.k (n) = Re [r.sub.k (n )] + j Im [r.sub.k (n)], and wherein the components Re [r.sub.k (n)] and Im [r.sub.k (n)] occur with a sampling period T/2. Thereafter these complex signals, possibly after having been processed further, are modulated on a complex carrier signal having a carrier frequency which is characteristic for the relevant modulation channel. For performing said selective modulation and for performing said modulation on the complex carrier signal each modulation channel is constructed as a digital Weaver-modulator wherein digital modulators, as well as digital filters are used. PA0 2. The second category includes those TDM-FDM-arrangements wherein no modulation processing is applied utilizing a carrier signal having a carrier frequency which is characteristic for the relevant signal {x.sub.k (n)}. In the TDM-FDM-arrangements of this category, use is made of the properties of a discrete signal, and more specifically of the fact that the frequency spectrum of a discrete signal has a periodical structure, the period being equal to the value of the sampling frequency 1/T of the baseband signal. An arrangement belonging to this second category has already been proposed in reference 4. It comprises N-signal channels, N being equal to the number of base-band signals. A baseband signal being applied to each of these signal channels. Each of the signal channels comprises means for increasing the sampling rate associated with the baseband signal by a factor of N to a value N/T. By increasing the sampling rate, a discrete signal {t.sub.k (n)} is obtained having a periodic frequency spectrum whose period is equal to, but whose fundamental intervals is equal to N/T (see chapter (1.2). Each interval of the length N/T of the frequency spectrum includes 2N subbands each having a width of 1/(2T). Each signal channel further comprises a discrete bandpass filter having a bandwidth 1/(2T). The passbands of the bandpass filter included in the successive signal channels coincide with the successive subbands of the first N subbands of the frequency spectrum of the discrete signal {t.sub.k (n)}. So the output signals {u.sub.k (n)} of the successive bandpass filters represent the desired channel signals for the baseband FDM-signal. PA0 means for receiving said baseband signals {x.sub.k (n)}; PA0 means for selectively modulating the received signals {x.sub.k (n)} for generating baseband signals {r.sub.k (n)}; PA0 a transformation device for processing said selectively modulated baseband signals {r.sub.k (n)} for generating a plurality of discrete conversion signals {s.sub.m (n)}, (m = 1, 2, 3, . . . N), said transformation device having associated therewith a transformation matrix A comprising the matrix elements a.sub.mk of a constant value and which transformation matrix is unequal to the Discrete Fourier Transform (DFT) matrix, and whereby the relation between the components s.sub.m (n) and the components r.sub.k (n) being given by ##EQU1## a plurality of signal channels to each of which a conversion signal is applied and which are each provided with discrete filter means and sampling rate increasing means for generating discrete signals {u.sub.m (n)}; the transfer function of the signal channel determined by said discrete filter means being equal to H.sub.m (.omega.); PA0 means for forming a digital sum signal ##EQU2## II. that for each signal channel the relation between its transfer function H.sub.m (.omega.) and the matrix elements a.sub.mk is given by the FDM-condition ##EQU3## wherein: m is the number of the relevant signal channel; PA0 means for receiving said signals {x.sub.k (n)}; PA0 a cascade arrangement of selective modulation means and complex modulation means, whose input is coupled to said receiver means and which is arranged for generating complex signals {r.sub.k (n)} with which complex modulation means a complex carrier signal having a frequency (.omega..sub.1 /2.pi.) is associated; PA0 a transformation device for processing said signals {r.sub.k (n)} and for generating a plurality of discrete conversion signals {s.sub.m (n)}, (m = 1, 2, 3, . . . N), said transformation device having associated therewith a transformation matrix A comprising the elements a.sub.mk of a constant value and which transformation matrix is unequal to the Discrete Fourier Transform (DFT)-matrix, and whereby the relation between the components s.sub.m (n) and the components r.sub.k (n) is given by ##EQU4## a plurality of signal channels, to each of which a conversion signal is applied and which are each provided with discrete filter means and sampling rate -- increasing means for generating discrete signals {u.sub.m (n)}; the transfer function of the signal channel determined by said discrete filter means being equal to H.sub.m (.omega.); PA0 means for forming a discrete sum signal ##EQU5## II. that for each signal channel the relation between its transfer function H.sub.m (.omega.) and the matrix elements a.sub.mk is given by the FDM-condition ##EQU6## wherein: m denotes the number of the relevant signal channel; PA0 means for receiving said discrete frequency division-multiplex-signal {y(n)}; PA0 a plurality of signal channels to each of which said discrete frequency-division-multiplex signal {y(n)} is applied and which are each provided with discrete filter means and sampling rate reduction means for generating discrete signals {s.sub.m (n)}; the transfer function of the signal channel determined by said filter means being equal to E.sub.m (.omega.); PA0 a transformation device to which said discrete signals {s.sub.m (n)} are applied and which is arranged for processing these signals for generating a plurality of discrete signals {r.sub.k (n)}; said transformation device having associated therewith a transformation matrix B comprising the matrix elements b.sub.km of a constant value and which transformation matrix is unequal to the Inverse Discrete Fourier Transform (IDFT) matrix and whereby the relation between the components s.sub.m (n) and the components r.sub.k (n) is given by: ##EQU7## an output circuit to which the signals {r.sub.k (n)} are applied and which is provided with means for selectively modulating the signals {r.sub.k (n)} for generating said discrete baseband signals {x.sub.k (n)}; PA0 means for receiving said frequency-division-multiplex-signal {y(n)}; PA0 a plurality of signal channels to each of which said discrete frequency-division-multiplex-signal {y(n)} is applied and each comprising discrete filter means and sampling rate reduction means for generating discrete signals {s.sub.m (n)}; the transfer function of the signal channel determined by said filter means being equal to E.sub.m (.omega.); PA0 a transformation device to which said discrete signals {s.sub.m (n)} are applied and which is arranged for processing these signals for generating a plurality of discrete signals {r.sub.k (n)}, said transformation device having associated therewith a transformation matrix B comprising the matrix elements b.sub.km of a constant value, said transformation matrix being unequal to the Inverse Discrete Fourier Transform (IDFT) matrix, whereby the relation between the components s.sub.m (n) and the components r.sub.k (n) is given by ##EQU9## an output circuit to which the signals {r.sub.k (n)} are applied and which comprises a cascade arrangement of selective modulation means and complex modulation means with which a complex carrier signal having the frequency (.omega..sub.1 /2.pi.) is associated, for generating said discrete baseband signals {x.sub.k (n)}; PA0 1. Digital signals. These signals are discrete time signals that can take on discrete amplitude values. Such signals are available in the form of a series of numbers which are each represented by a given number of bits. PA0 2. "Sampled data" signals. These signals are discrete time signals that can take on a continuum of amplitude values. For storing such signals "charge coupled devices" (CCD's) are, for example, used.
It is noted that in reference 5, a TDM-FDM-arrangement is described which is equivalent to the TDM-FDM-arrangements described in the references 3 and 4. Particularly the TDM-FDM-arrangement disclosed in reference 5 comprises only one single-sideband modulation channel, which for the various base-band signals {x.sub.k (n)} is operated in time sharing.
This equivalency also applies to what follows hereinafter.
The input circuit of this known arrangement also comprises means for selectively modulating the signals {x.sub.k (n)}. In this particular case, this means that either the components of the signals {x.sub.k (n)} having an even number k, or those having an odd number k are multiplied by a factor (-1).sup.n. The result of this multiplication is described in chapter E(1.3).